In binary regression, symmetric links such as logit and probit are usually considered as standard. However, in the presence of unbalancing of ones and zeros, these links can be inappropriate and inflexible to fit the skewness in the response curve and likely to lead to misspecification. This is the case of covering some type of insurance, where it can be observed that the probability of a given binary response variable approaches zero at different rates than it approaches one. Furthermore, when usual links are considered, there is not a skewness parameter associated with the distribution chosen that, regardless of the linear predictor, is easily interpreted. In order to overcome such problems, a proposal for the construction of a set of new skew links is developed in this paper, where some of their properties are discussed. In this context, power links and their reversal versions are presented. A Bayesian inference approach using MCMC is developed for the presented models. The methodology is illustrated considering a sample of motor insurance policyholders selected randomly by gender. Results suggest that the proposed link functions are more appropriate than other alternative link functions commonly used in the literature. Copyright © 2016 John Wiley & Sons, Ltd.

The objective of this study was to describe spatial and space-time patterns of type 1 diabetes in children less than 15 years old, diagnosed between 2000 and 2005 with residence in the Metropolitan Region of Chile. Knox and Mantel tests were used to detect space-time interaction between cases. An ecological Bayesian model adjusted by socioeconomic factor and year was proposed to estimate the incidence by communes. Initially, there was no space-time interaction between cases, but there is evidence of clustering effect in urban areas of the region. The incidence rate for the overall study period was estimated by 6.18/100,000 (95% CI: 5.69-6.70), with a significant annual trend of 8.2% (P < 0.01). The geographical incidence could be explained by the human development index, as a socioeconomic factor. These results suggest that children living in communes with higher socioeconomic levels may be at higher risk of developing type 1 diabetes. Our findings support the hypothesis of an aetiological role of environmental factors in the onset of type 1 diabetes.

No abstract